This journal is c the Owner Societies 2012 Phys. Chem. Chem. Phys., 2012, 14, 16595–16602 16595

Cite this: Phys. Chem. Chem. Phys., 2012, 14, 16595–16602

Hydrogen interaction with the anatase TiO2(101) surface

Ulrich Aschauer*w and Annabella Selloni

Received 5th July 2012, Accepted 8th August 2012

DOI: 10.1039/c2cp42288c

The interaction of atomic hydrogen with the majority (101) surface of anatase TiO2 is studied

using density functional theory calculations both with a standard semi-local functional and with

the inclusion of on-site Coulomb repulsion terms. We investigate the energetics of different

adsorption configurations at surface and subsurface sites and different coverages, from low to one

monolayer, as well as diffusion pathways among the different sites and recombinative H2

desorption barriers. While H2 desorption is the energetically most favorable process, the diffusion

of H into the subsurface is found to be at least equally favorable kinetically. It is further shown

that subsurface oxygen vacancies on reduced anatase are favorable adsorption sites for

hydrogen atoms.

TiO2 is an important technological material with widespread

applications in photocatalysis, photovoltaics, and self-cleaning

surfaces.1,2 Among the various TiO2 polymorphs, rutile is the

stable bulk phase, while anatase is stable in nanomaterials3

and has a higher photocatalytic activity.4 Hydrogen is a

typical reducing agent and has an important influence on the

electronic properties of TiO2.5,6 Unlike H2, which interacts

only weakly with bare TiO2 surfaces, atomic H readily adsorbs

forming surface hydroxyls. In particular, single-crystalline

TiO2 surfaces prepared with standard surface science cleaning

procedures frequently contain adsorbed hydrogen,5 which can

therefore affect their reactivity. For the widely investigated

rutile TiO2(110) surface, it was recently shown that adsorbed

H atoms can diffuse from the surface toward the bulk, and this

process is kinetically favored compared to H2 desorption.7 In a

subsequent experimental study, it was found that hydrogen

can be incorporated into anatase TiO2 nanoparticles where it

leads to a significant band gap reduction hence efficient

photocatalytic activity under visible light.8 More recently,

hydrogen incorporation and storage in well-defined anatase

nanocrystals with predominant (001) and (101) surface terminations

was investigated.9 It was found that hydrogen can incorporate and

store in anatase TiO2, and the storage capacity of samples with

predominant (101) terminations is B40% higher than that of

nanocrystals with a high percentage of (001) facets under the

experimental conditions used (450 1C, hydrogen pressure of

7.0 MPa).

Hydrogen incorporation in anatase TiO2 is also supported

by recent computational studies.9,10 In particular, Islam et al.

showed that hydrogen can pass through the anatase TiO2(101)

surface and incorporate into the TiO2 lattice with barriers of

about 2 eV.10 Due to the use of a relatively small surface unit cell,

however, only high coverage conditions and, more importantly,

only a subset of the possible hydrogen migration and reaction

pathways were considered in ref. 9 and 10. In the present study

we obtain further insight into the behavior of hydrogen on

anatase(101), by comprehensive DFT and DFT + U11 calcula-

tions of atomic H adsorption, desorption and incorporation at

different coverages. Several possible surface and subsurface H

adsorption sites, including defects, are considered, and diffusion

pathways between these sites are determined at both DFT

and DFT + U levels. Finally, the influence of surface and

subsurface hydrogen on the adsorption of water, a typical

probe molecule, is investigated.

Anatase TiO2(101) is the most stable and frequently exposed

surface of anatase. It shows under-coordinated five-fold Ti

(Ti5c) and two-fold O (O2c) atoms, as well as fully coordinated

Ti6c and two types of O3c sites (Fig. 1). As discussed below,

Fig. 1 O sites (A to D) within the surface and subsurface region of the

3 layer anatase slab employed in the present study. Layers are separated

by dashed lines and numbered from 1 to 3. Only sites considered in this

study are labeled. Color code: Ti = grey, O = red.

Department of Chemistry, Princeton University, Princeton,New Jersey 08544, USAw Present address: Materials Theory, ETH Zurich, 8093 Zurich,Switzerland. E-mail: uli.aschauer@mat.ethz.ch

PCCP Dynamic Article Links

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16596 Phys. Chem. Chem. Phys., 2012, 14, 16595–16602 This journal is c the Owner Societies 2012

hydrogen adsorption takes place at the oxygen sites. Four

inequivalent O sites exist in each TiO2 layer, which will be

referred to by letters from A to D and prefixed with the

number, 1 to 3, of their layer, see Fig. 1. Site 1A is the two-

fold coordinated surface oxygen, whereas sites 1B and 1C are

higher and lower lying three-fold coordinated surface oxygen

ions, respectively. Site 1D is a three-fold coordinated oxygen

at the bottom of the first TiO2 layer. All sites in the second

layer are fully coordinated but differ in their local atomic

environment and in their relative position with respect to the

surface. In the present study we only consider sites above

approximately the mid-plane of the slab employed for the

calculations (Fig. 1), in order to minimize spurious effects

coming from the bottom surface.

Adsorption: in the following we refer to the situation of a

typical surface science experiment in which atomic H is

generated using a hot filament to dissociate H2 before it

interacts with the surface. The computed energetics, however,

apply also to experiments where the source of H is molecular

H2 (see below) or water dissociatively adsorbed on the surface,

see ref. 12. Atomic hydrogen impinging on the surface from

the gas phase could in principle adsorb to any of the exposed

oxygen or titanium sites. However, no local minimum corre-

sponding to adsorption at a surface Ti5c site was found, as H

desorbed spontaneously. Therefore we only consider adsorp-

tion on the oxygen 1A, 1B or 1C sites (Fig. 1). In bulk anatase,

H may adsorb to a lattice O either in a position in plane or out

of plane with respect to the three O–Ti bonds, the latter being

more favorable by about 0.5 eV.13 At the surface one should

also consider whether the OH bond points towards the

vacuum or away from it. We performed calculations for all

possible configurations, and in Table 1 we list the most

favorable adsorption energies for each site and at different

coverages, computed at the PBE (PBE + U) level with respect

to both atomic H and molecular H2. From these data, site 1A

emerges as the most favorable adsorption site at 1/6 ML

coverage, with an energy gain of 2.15 (2.30) eV relative to an

H atom in gas phase. This value agrees well with the one, 2.31 eV,

previously reported in ref. 10. The energy gain upon adsorption

of atomic H is substantial and competitive to that resulting

from H2 formation: two H atoms would prefer to form H2 by a

mere 0.07 eV within PBE, whereas bonding to the anatase

surface is predicted to be slightly preferred, by 0.08 eV, within

PBE + U.

From Table 1, we can see that the overall trends in the

stability of different adsorption sites are the same at the PBE

and PBE + U levels. Some differences can be understood

considering the different description of the state of the H

electron within the two approaches. Upon H adsorption, the

electron from the H atom forms a localized polaronic state

with energy below the bottom of the conduction band according

to the PBE + U approach, whereas it forms a delocalized

conduction band state according to pure PBE.13 For instance,

compared to 1A, sites 1B and 1C are less favorable for H

adsorption, and the difference in favor of 1A is more evident at

the PBE+U level. This is likely because for adsorption at 1A,

PBE + U predicts that the H electron localizes at the surface,

where the polaronic distortion is somewhat easier, whereas it

localizes in the subsurface for the other sites.

It is also interesting to note that the minimum energy

configuration for H at site 1C is characterized by the OH

bond pointing away from the vacuum towards the bulk

(Fig. 2c) whereas at the other two sites the OH points towards

the vacuum (Fig. 2a and b). Since it is unlikely that H would

arrive at 1C in the H-down configuration, Table 1 reports also

the adsorption energy of the metastable 1Cm state, where H

points towards the vacuum. The transition between the metastable

and the stable structure is discussed in detail below.

Turning now to the adsorption energies at 1/3 and 1 ML

coverage in Table 1, we can see that combinations including site

1A are largely favored. The interaction between H atoms adsorbed

at 1A sites is weak. In fact, the PBE adsorption energies for 1A

(1/6 ML), 1A + 1A (1/3 ML) and 6 � 1A (1 ML) have values

of �2.15, �2.10, and �2.01 eV, respectively. At the PBE + U

level a slight decrease in adsorption energy is observed from

1/6 ML (�2.30 eV) to 1/3 ML (�2.16 eV), whereas the

full monolayer is nearly as favorable as the 1/6 ML

(�2.29 eV). This can be related to the localization of the

Table 1 Adsorption energies per atom for hydrogen adsorbed on theanatase(101) surface in various configurations and coverages, computedat the PBE (PBE+ U) level. For U, the value U = 3.5 eV, as obtainedby linear response, is used.14,15 DEads,H and DEads,H2

are the adsorptionenergies (in eV) relative to atomic H and molecular H2 in the gas phase,respectively. Negative values of the adsorption energy indicate that theadsorbed state is energetically favorable relative to the correspondingnon-interacting reference

Coverage Configuration DEads,H DEads,H2

1/6 ML 1A �2.15 (�2.30) 0.07 (�0.08)1B �1.66 (�1.47) 0.56 (0.76)1C �1.83 (�1.64) 0.39 (0.58)1Cm �1.69 (�1.47) 0.53 (0.75)

1/3 ML 1A + 1A �2.10 (�2.16) 0.13 (0.06)1A + 1B �1.79 0.431A + 1Cm �1.87 0.351B + 1B �1.38 0.851B + 1Cm �1.55 0.681Cm + 1Cm �1.46 0.77

1 ML 6 � 1A �2.01 (�2.29) 0.21 (�0.06)

Fig. 2 (a)–(c) Minimum energy configurations for H adsorption at

the 1A, 1B and 1C site, respectively, (d) metastable configuration 1Cm

with hydrogen pointing outwards.

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H electrons: at 1/6 ML the H electron localizes on the Ti6c near

the proton; at 1/3 ML the electrostatic repulsion between the

two electrons causes one of them to move to the adjacent row,

away from the protons; at 1 ML all Ti6c carry one extra electron

and a situation similar to the 1/6 ML case is recovered.

As shown in Fig. 2a, H adsorbed at site 1A slightly leans to

one side, so that at higher coverages neighboring H atoms can

adopt configurations either pointing towards each other

or apart. The computed energy barrier for the flip of a single

H from one side to the other is extremely small, B0.05 eV. An

8 ps Car–Parrinello16 molecular dynamics simulation at

220 K was used to sample the dynamic arrangement of two

neighboring H atoms. The resulting H–H distance probability

distribution is shown in Fig. 3. Two states predominantly

exist, one less important where the two H point apart and a

more frequent one where the two adsorbed hydrogens point in

the same direction. Instead, the situation where the two H point

towards each other was not observed on the time-scale of the

dynamics. This suggests that at higher coverages (i.e. full ML) all

adsorbed H will predominantly point in the same direction.

Surface diffusion of adsorbed H: we computed the minimum

energy pathways for diffusion between all surface sites at 1/6 ML

coverage (1 H atom per surface cell). The resulting barriers are

given in Table 2. Comparison with ref. 10 shows a good agreement

for the 1B - 1Cm barrier, whereas the barrier for the 1A - 1B

migration is considerably lower than previously reported. The

discrepancy may be due to the more favorable adsorption at

site 1B predicted in the present work.

The computed H migration barriers are rather low indicating

that adsorbed H atoms should be mobile at room temperature.

In particular, diffusion of H along [010] rows (barrier of 0.60 eV)

is predicted to be much faster than across rows (combined barrier

of 1.82 eV), see Fig. 4. Diffusion perpendicular to the rows

occurs preferentially in the zigzag sequence shown in Fig. 4, as

direct diffusion between sites 1A and 1B to its left as well as

site 1Cm and the site 1A to its left is highly unfavorable due to

the proximity of Ti atoms.

Recombinative H2 desorption: the computed adsorption energies

in Table 1 indicate that recombinative H2 desorption becomes

increasingly favorable with increasing hydrogen coverage.

(The trend is less clear at the PBE + U level due to the

increased stability of the full monolayer.) However, the viability

of the H2 desorption reaction at a given temperature is mainly

determined by the associated energy barrier. We computed the H2

desorption barriers for different configurations at 1/3ML and full

ML using the climbing image NEB method,17 see Table 3. At the

PBE level desorption is more favorable not only energetically but

also kinetically at higher coverage, as can be seen by comparing

the values for the 1A + 1A case at 1/3 ML with the 6 � 1A case

at 1 ML. It appears that most barriers are in the range of 1.8 to

2 eV, which makes them hardly accessible at room temperature.

In particular, the 1A + 1C desorption pathway is in good

agreement with the one predicted in ref. 10. We also found a

low (1.39 eV) barrier desorption channel for the 1A + 1B

configuration, which was not considered in previous work. Since

barriers for surface diffusion are typically below 1 eV, diffusion

into favorable configurations and subsequent desorption may be

more likely than direct desorption.

Due to increased computational cost, only the most favor-

able desorption barrier from the 1A + 1B configuration has

been computed at the PBE + U level. The barrier increases

slightly by 0.09 eV, while the energy difference between the

adsorbed and desorbed state is reduced by more than 0.5 eV

with respect to the PBE results. This is due to the stabilization

of the 1A adsorption site at the PBE + U level (see Table 1)

and indicates that the transition state is also stabilized by a

comparable amount of energy.

Fig. 3 Probability distribution of the H–H bond length for two

adsorbed H atoms in the 1A + 1A configuration (1/3 ML coverage).

Table 2 Forward (-) and reverse (’) diffusion barriers and energydifference (DE) for diffusion between different surface sites at 1/6 MLhydrogen coverage. All values are in eV

Coverage From To -Barrier ’Barrier DE

1/6 ML 1A 1A 0.60 0.60 0.001A 1B 0.96 0.47 0.501A 1Cm 0.72 0.26 0.461B 1Cm 1.32 1.36 �0.04

Fig. 4 Minimum energy pathways for H diffusion along the [010]

(green) and [101] (blue) directions on the anatase(101) surface at

1/6 ML coverage.

Table 3 Barrier for H2 desorption and corresponding energy gain DEdes

computed at the PBE (PBE + U) level. Different coverages (1/3 and1 ML) and combinations of H adsorption sites are considered. Negativevalues of DEdes indicate that desorption is energetically favorable. Allvalues are in eV. The 1B + 1B and 1Cm + 1Cm configurations evolvespontaneously to 1A + 1B and 1A + 1Cm, respectively, by diffusionof one of the two H atoms to 1A

Coverage Configuration Barrier DEdes

1/3 ML 1A + 1A 2.01 �0.26 (�0.12)1A + 1B 1.39 (1.48) �0.88 (�0.32)1A + 1Cm 2.03 �0.721B + 1B - 1A + 1B1B + 1Cm 1.80 �1.391Cm + 1Cm - 1A + 1Cm

1 ML 6 � 1A 1.87 �0.43 (+0.12)

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The desorption pathways from the 1A + 1A and 1A + 1B

configurations are compared in Fig. 5. In the former case, both

H atoms approach and their bonds are stretched simultaneously

until H2 is formed and desorbs. The simultaneous breaking of

two O–H bonds is at the origin of the high desorption energies

for this configuration. In the 1A + 1B case, the H atom

adsorbed at site 1B (shown in green) desorbs first, which

represents the transition state of the reaction, and migrates to

a position above the neighboring Ti5c site. The second H bound

to 1A then approaches, H2 is formed and desorbs.

The results in Table 3 and Fig. 5 are calculated for a

desorbing H2 molecule at 0 K and therefore neglect the entropic

contributions to the free energy of the molecules in gas phase.

This can be estimated from tabulated thermochemical data,18,19

using the following expression for the chemical potential of

species X as a function of temperature and partial pressure:

mX ¼1

AEtotXAþ ~mXA

ðT ; p0Þ þ kT lnpXA

p0

� �� �

The letter A is used to indicate the stoichiometry of species

X in the tabulated gas phase compound XA (for instance, for

X = H, the gas phase species is XA = H2, so that A = 2).

Values for mH2and mH2O

are given in Table 4. The negative

temperature dependence of mH2will stabilize the desorbed

state and favor H2 desorption at finite temperature. Low H2

partial pressure also favors H2 desorption. Since the transition

state consists of H fragments still bound to the surface,

the effect of the free energy on the kinetics should be less

pronounced. However, H2 desorption obviously becomes

increasingly favorable with increasing temperature.

Defect formation via H2O desorption: an interesting adsorp-

tion configuration, not considered in Table 1, is shown in

Fig. 6. In this configuration (denoted 2H@1A) two hydrogen

atoms are adsorbed on the same 1A site. There is also a

marked outward relaxation of the 1A adsorption site together

with a smaller inward relaxation of the neighboring O2c atoms

in the same row. The computed adsorption energy per H atom

is �1.75 eV relative to atomic H in gas phase, a value close to

those found for the 1A + 1B and 1A + 1Cm configurations

(see Table 1). This suggests that the 2H@1A configuration

may occur at higher coverage, when all surface sites (1A, 1B,

1Cm) are singly occupied with H.

Starting from the configuration in Fig. 6, H2 desorption is

found to be exothermic by 0.94 eV and the computed barrier is

2.08 eV. For this configuration we also examined desorption

of an H2O molecule resulting in the formation of an oxygen

vacancy at site 1A. The latter reaction is endothermic by about

1.2 eV, with no additional energy barrier, and the final state

with a surface oxygen vacancy and a gas phase water molecule

is 2.12 eV higher in energy relative to the stoichiometric

surface plus H2 in the gas phase. This suggests that H2O

desorption with surface oxygen vacancy formation is likely to

Fig. 5 Trajectory of H2 desorption from 2 adsorbed H. Top: 1A + 1A

configuration. Bottom: 1A + 1B configuration. For both configurations

the potential energy evolution for theminimum energy desorption pathway

is shown; key configurations are highlighted in yellow, orange and brown

disks, corresponding to larger spheres of same color in the H trajectories

(green and purple spheres) on the left side. Also shown are the HOMO

charge densities of a few configurations.

Table 4 Vibrational, rotational and ideal gas entropy contributionsto the chemical potential of H2 and H2O in a relevant temperaturerange.19 p0 is the standard pressure, p0 = 1 bar

T/K mH2(T, p0)/eV mH2O

(T, p0)/eV

100 �0.07 �0.12200 �0.19 �0.30300 �0.32 �0.48400 �0.46 �0.69500 �0.61 �0.90600 �0.76 �1.11700 �0.92 �1.34800 �1.08 �1.57

Fig. 6 Adsorption configuration with two H bound to the same 1A

site. Ti–O bonds (2.24 A, 2.68 A) are significantly stretched compared

to the case without H atoms (1.81 A, 1.90 A) while the O–H bonds are

equivalent to those in gas phase water (0.99 A) and the tetrahedral

angle is slightly larger (110.61 vs. 104.51).

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remain unfavorable at all temperatures of interest, even though

the free energy contributions (Table 4) tend to stabilize the

desorbed water molecule more than H2. However, the like-

lihood that H2 reacts with an O2c site to form H2O and oxygen

vacancies should increase when the surface is exposed to H2 at

high pressures, a procedure sometimes used in technological

applications.5,8

In order to assess this high H2 pressure regime, we carried

out simulations where the 10 A thick vacuum layer above the

surface was filled with 10 H2 molecules, corresponding to a H2

partial pressure of nearly 600 bar. We used this pressure,

which is significantly higher than that of typical experiments,

with the purpose to accelerate the reactions and make them

observable within the limited time scale of our simulations;

still, the mechanisms for H2 interaction with the surface

should not be significantly different from those which are

present at lower pressure. Starting from the 2H@1A configuration

with the remaining nine H2 filling the vacuum gap (Fig. 7a), we

performed 400 K Car–Parrinello16 molecular dynamics simula-

tions. A rapid outwards relaxation of the ‘‘water molecule’’ was

observed, resulting in the formation of an oxygen vacancy at the

surface (Fig. 7b). This vacancy first showed the known tendency

of migrating towards the subsurface20,21 but then reacted within

2.8 ps with the just formed ‘‘water molecule’’, resulting in

dissociated water, as previously predicted12 (Fig. 7c). It thus

seems to be possible for the 2H@1A configuration to decay into

a configuration with two adsorbed hydrogens at very high H2

pressure (Fig. 7d).

Surface to subsurface diffusion: H adsorption energies at

subsurface O sites, evaluated at 1/6 ML coverage at both the

PBE and PBE + U levels, are reported in Table 5. Comparison

with the results in Table 1 shows that these energies are of the

same order as the adsorption energies at the 1B and 1C surface

sites. Moreover, while H is clearly most stable at 1A surface sites,

migration from the surface sites 1B, 1Cm into the subsurface

site 2A is energetically favorable.

Diffusion pathways from the surface to the subsurface were

determined by a series of NEB calculations and the resulting

energy barriers are given in Table 6. We first consider the

migration of an H atom at 1/6 ML coverage computed at the

PBE level. With an activation barrier in excess of 2.5 eV and a

significant increase in energy of 0.7 eV, the migration of an H

atom from site 1A directly to the subsurface site 1D is clearly

unfavorable. The most favorable pathway to the subsurface is

via site 1C, where migration from the meta-stable state in which

H points outwards to the stable state in which H points inwards

requires a barrier of only 0.5 eV and is accompanied by a gain in

energy of 0.13 eV. The minimum energy surface - subsurface

diffusion pathway at 1/6 ML coverage is shown in Fig. 8.

Starting from its initial surface adsorption site (1A, 1B or

1Cm), an H atom should first migrate towards the closest 1Cm

site. Diffusion from site 1A to site 1Cm proceeds with a barrier

of 0.72 eV, whereas an H atom at site 1B should first diffuse to

site 1A (barrier of 0.96 eV). Diffusion into the subsurface occurs

by migration from site 1Cm to site 1C with a barrier of 0.54 eV,

which is followed by a transition from sites 1C to 2A, which

has a barrier of only 0.21 eV.

At the PBE + U level, adsorption at site 1A becomes 0.15 eV

more favorable, site 2A remains almost unchanged, whereas

adsorption at the other sites becomes less favorable by B0.2 eV.

Interestingly, the energies of the transition states for the 1B- 1A,

1A - 1Cm and 1C - 2A pathways are found to be almost

unaffected by the +U correction. However we can see the

appearance of double-peaks in the +U pathways. The origin

of this barrier splitting is illustrated at the bottom of Fig. 8 for

Fig. 7 Snapshots of a molecular dynamics simulation at 400 K in the

presence of 2H@1A and 9H2 molecules in gas phase: (a) the 2H@1A

configuration, (b) desorbing water bound to a Ti5c next to a surface

oxygen vacancy, (c) water dissociation and tendency for the surface

oxygen vacancy to go subsurface and (d) healing of the oxygen

vacancy by the OH fragment to form two adsorbed H on the defect

free surface.

Table 5 Adsorption energies for H on different subsurface O sites(see Fig. 1) at 1/6 ML coverage, computed at the PBE (PBE + U)level. DEads,H and DEads,H2

are the adsorption energies (in eV) relativeto atomic H and molecular H2 in the gas phase, respectively

Site DEads,H DEads,H2

1D �1.42 (�1.82) 0.80 (0.40)2A �1.89 (�1.87) 0.34 (0.36)2B �1.77 (�1.57) 0.45 (0.65)2C �1.77 (�1.56) 0.45 (0.66)Bulk13 0.39 (0.47–0.58)

Table 6 Diffusion barriers for various path segments leading to Hmigration into the subsurface at different coverages (1/6, 1/3 and1 ML). For 1/3 and 1 ML coverages, pathways in which H at aneighboring 1A site leans either away or towards the diffusing H atomare possible; the configurations are indicated as far and close respec-tively. Barriers computed at the PBE + U level are given in parenth-esis. All values are in eV

From To Coverage -Barrier ’Barrier DE

1A 1D 1/6 ML 2.53 (2.37) 1.80 (1.89) 0.73 (0.48)1/3 ML far 2.60 1.74 0.861/3 ML close 2.58 1.36 1.22

1B 1D 1/6 ML 0.96 0.73 0.231Cm 1C 1/6 ML 0.54 (0.57) 0.68 (0.77) �0.13 (�0.20)

1/3 ML far 0.59 0.63 �0.041/3 ML close 0.57 0.53 0.041/1 ML far 0.64 0.45 0.191/1 ML close 0.47 0.49 �0.02

1C 2A 1/6 ML 0.21 (0.41) 0.27 (0.62) �0.06 (�0.21)1/3 ML far 0.20 0.32 �0.121/3 ML close 0.14 0.33 �0.191/1 ML far 0.00 0.45 �0.441/1 ML close 0.00 0.47 �0.47

1D 2A 1/6 ML 0.44 0.90 �0.461/3 ML far 0.95 1.42 �0.471/3 ML close 0.95 1.42 �0.47

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16600 Phys. Chem. Chem. Phys., 2012, 14, 16595–16602 This journal is c the Owner Societies 2012

the example of the 1A - 1Cm transition. It can be seen that

the first peak of the barrier is associated with the ionic

rearrangements, whereas the subsequent smaller barrier originates

from the relocation of the H electron. Altogether, the energy

barrier computed at the +U level for the 1A - 2A pathway

increases by the sum of the 1A stabilization and 1Cm destabi-

lization energies, i.e. B0.4 eV. PBE + U therefore predicts

surface - subsurface diffusion kinetics to be significantly

slower than standard PBE.

At higher coverages (1/3 and 1/1 ML) pathways in which H

at a neighboring 1A site lean away or towards the diffusing H

atom are possible, see Table 6. The difference in barrier

between the two cases is usually small and of the order of

the DFT error. One exception is the jump from 1A to 1D, for

which at 1/3 ML coverage the 1D adsorption site is 0.36 eV

less favorable in the ‘close’ configuration. Instead, a pathway

becoming more favorable when the two H are closer is the

migration from the metastable 1Cm to the 1C site. This may be

related to the fact that the H atom adsorbed on site 1Cm causes a

slight outward relaxation of the H atom at the nearby 1A site.

The tendency of this 1A bound H atom to return to its

equilibrium position will help the migration of H at 1Cm into

1C, as illustrated in Fig. 9.

Most of the surface - subsurface pathways like 1A - 1D,

1Cm - 1C and 1D - 2A require larger activation energies

with increasing coverage. The 1C - 2A pathway however

shows a decreasing barrier with increasing coverage, which

even vanishes at full ML coverage. This is due to a more

pronounced inward relaxation of the site 1C atom at higher

coverages, which leads to a significant shortening (1.89 A at

1/6 ML to 1.65 A at 1 ML) of the distance between site 2A and

the H atom and consequently easier transfer of the H atom.

In summary, our results indicate that although the most

favorable H adsorption is at the surface O2c sites (site 1A), the

increase in energy associated with migration into subsurface

sites is small. As the number of bulk sites is much larger than

the number of surface sites, there is also a favorable entropic

component to the free energy of incorporation into the bulk. It

is noteworthy that at the PBE as well as PBE + U level

the energy barriers associated with surface - subsurface

diffusion (PBE B 1.0 eV, PBE + U B 1.5 eV) are either of

the same order (1A+ 1B: PBEB 1.4 eV, PBE+UB 1.5 eV)

or smaller than those associated with H2 desorption (PBE

1.8–2.0 eV for combinations other than 1A + 1B). Therefore

migration of at least part of the H adsorbed at the surface

towards the subsurface should be kinetically favorable, espe-

cially at higher coverage when the 1A sites tend to be occupied

and adsorption at the remaining surface sites (1B, 1Cm) is less

favorable than in the subsurface. These results also suggest

that, under the condition that H stored in the bulk can be

released, anatase could have applications in hydrogen storage.

H at subsurface oxygen vacancies: H adsorption at O vacancies

has been proposed to occur in some oxide materials22 and in bulk

anatase23 and rutile24 as well. It is therefore interesting to explore

the possibility of H adsorption at subsurface oxygen vacancies,

which have been shown to be quite frequent at the reduced

anatase(101) surface.20,21,25 We computed the adsorption energy

of a single H substituted for O at site 2A, which is the most

favorable subsurface vacancy position,20,21 and found it to be

�0.30 eV relative to H2 (or �2.52 eV relative to H) at the PBE

level, thus more stable than at any other adsorption site in Table 1.

Fig. 8 Most favorable surface - subsurface migration pathway at

1/6 ML coverage calculated at the PBE and PBE+U level. Possible H

adsorption sites (1B, 1A, 1Cm) are indicated by arrows. Diffusion

towards the subsurface could start at any of these sites. The diffusion

pathway from sites 1B to 1Cm is not shown due to the large energy

barrier (1.3 eV at the PBE level). The structures at the bottom show

the double-barriers at the PBE + U level resulting from migration of

the ions followed by the localized extra-electron (visualized as the

HOMO charge density shown in blue).

Fig. 9 Selected configurations along the H diffusion pathway from

1Cm to 1C at 1 ML coverage: (a) H at 1Cm in the presence of 5 other H

atoms, with the neighboring H (circled in green) at 1A relaxed

upwards; (b) transition state of the 1Cm–1C migration, with the 1A

bound H returning to its equilibrium position; (c) H bound to site 1C

with the 1A bound H at its equilibrium position.

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This journal is c the Owner Societies 2012 Phys. Chem. Chem. Phys., 2012, 14, 16595–16602 16601

At the PBE + U level, the adsorption energy at the vacancy

site is +0.08 eV relative to H2 (or �2.14 eV relative to H), a

stability similar to the one at the most favorable 1A surface

site. These results suggest that, when entropic contributions

due to the larger number of bulk sites are taken into account,

H on reduced TiO2 is likely to migrate into subsurface O

vacancies at least at high H coverages.

An effect of subsurface and surface H on water adsorption: for

completeness, we have also considered the influence of surface

and subsurface hydrogen on the surface reactivity focusing on

water, a typical probe molecule. As seen above, subsurface H

may either be adsorbed to an O atom or at an oxygen vacancy

in the case of reduced anatase surfaces. Table 7 reports water

adsorption energies at all Ti5c sites above these two types of

subsurface H atoms (H adsorbed to site 2A (Fig. 10a) and H

substituted on site 2A (Fig. 10b)) and in the presence of an H

atom at the surface 1A site (Fig. 10c).

The water adsorption energy on the stoichiometric surface

without any adsorbed H is �0.72 eV.12 In the presence of H

adsorbed to a subsurface 2A site, the water adsorption energy

is usually slightly lower than on the stoichiometric surface.

There seems to be a correlation of the water adsorption energy

with the distance to the subsurface H atom, the two furthest

sites recovering the adsorption energy of the stoichiometric

surface. In the presence of H in a subsurface oxygen vacancy, a

slightly more favorable adsorption than for the stoichiometric

surface is observed. In proximity of H at a 1A site, two distinct

situations occur on the 3 � 1 slab, depending on whether the

water adsorbs in the row to the left (on the periodically

repeated slab) of the adsorbed H or to its right. Adsorption

to the right, where no H-bonds are formed between water and

the O2c row on which H is located, is more favorable than on

the stoichiometric surface, whereas the opposite is true for

water adsorbed on the left side. The most favorable adsorption

at site 3 goes along with one significantly shortened H-bond,

while the other H-bond gets longer. Water at site 4, which has

none of its H-bonds to O2c directly affected by the adsorbed H,

nearly recovers the adsorption energy of the stoichiometric

surface, whereas the two other sites see a lowering in their

adsorption energy due to the presence of H at the surface. The

effect is more marked for site 5, the site towards which the

adsorbed H leans, which entirely disables H-bonding thus

leading to a very long H–O2c distance. Given however the

low energy barrier associated with flipping the adsorbed H

from one side to the other, it is likely that a more favorable

water adsorption configuration equivalent to site 6 can be

easily recovered.

In conclusion, we have investigated the adsorption and

diffusion of hydrogen on the anatase(101) surface by means

of first-principles calculations. The main result is that hydrogen

migration from surface to subsurface sites has kinetic barriers

which are generally smaller than those of H2 desorption. The

same result has been reported in a recent study,10 but our

computed energy barriers for surface - subsurface diffusion

are significantly lower compared to those obtained in ref. 10,

implying that the effect should be more rapid than previously

predicted. The H adsorption energy at subsurface sites is

B0.4 eV smaller relative to that at surface O2c sites, however

subsurface adsorption is entropically favored. Atomic hydrogen

is therefore likely to diffuse into the subsurface and further into

the bulk, especially at higher coverage when less favorable

surface sites are also likely to be occupied.

An additional result of this work is that subsurface vacancies,

which are stable in reduced anatase, can favorably accommodate

hydrogen. This suggests that hydrogen incorporation into the bulk

could be enhanced in highly reduced samples, an effect that may be

useful for technological applications like hydrogen storage.9 Such

subsurface vacancy bound Hmakes water adsorption slightly more

favorable compared to the stoichiometric surface. A similar effect is

observed in the presence of surface bound H while no such effect is

present for H adsorbed at regular subsurface sites.

Table 7 Water adsorption energies at all non-equivalent sites above a H atom adsorbed to site 2A on the stoichiometric surface or above an Hatom substituted for site 2A (into the vacancy) for the reduced surface

Site

H adsorbed at site 2A H substituted for O at site 2A H adsorbed at site 1A

DEads [eV] Ti5c–O [A] H–O2c [A] H–O2c [A] DEads [eV] Ti5c–O [A] H–O2c [A] H–O2c [A] DEads [eV] Ti5c–O [A] H–O2c [A] H–O2c [A]

Site 1 �0.71 2.30 2.22 2.22 �0.73 2.30 2.21 2.21 �0.74 2.29 2.29 2.26Site 2 �0.68 2.30 2.18 2.46 �0.72 2.29 2.14 2.33 �0.74 2.30 2.35 2.23Site 3 �0.69 2.30 2.43 2.14 Symmetry equivalent to site 2 �0.76 2.30 2.13 2.39Site 4 �0.72 2.29 2.24 2.19 �0.73 2.30 2.22 2.18 �0.71 2.29 2.30 2.36Site 5 �0.70 2.30 2.22 2.24 �0.73 2.28 2.21 2.20 �0.57 2.29 2.38 2.88Site 6 �0.72 2.29 2.23 2.23 Symmetry equivalent to site 4 �0.70 2.29 2.24 2.36

Fig. 10 Ti5c sites numbered from 1 to 6 for water adsorption, (a) for a

H atom adsorbed to a subsurface 2A site (stoichiometric surface),

(b) for a H atom in a subsurface oxygen vacancy (reduced surface) and

(c) in the presence of a H adsorbed at site 1A, (d) shows a side view of

the structure in (b), where it can be seen that H is accommodated in the

oxygen vacancy without significant structural distortions.

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16602 Phys. Chem. Chem. Phys., 2012, 14, 16595–16602 This journal is c the Owner Societies 2012

Computational details

We carried out spin-polarized DFT calculations within the

Generalized Gradient Approximation (GGA) of Perdew,

Burke and Ernzerhof (PBE),26 both without and with the

inclusion of on-site Coulomb repulsion U on the Ti 3d states.11

For the PBE + U calculations we used the computed U value

of 3.5 eV.6,13,15,27,28 The plane-wave pseudopotential scheme as

implemented in the Quantum ESPRESSO package was

employed.29 Electron–core interactions were described by

ultra-soft pseudopotentials30 with Ti(3s, 3d, 3p, 4s), O(2s, 2p)

and H(1s) shells treated as valence electrons. Wave functions

were expanded in plane waves up to a kinetic energy cutoff of

25 Ry while using a cutoff of 200 Ry for the augmented density.

We modeled the anatase(101) surface as a three layer thick slab

with a 3 � 1 surface supercell (10.262 A � 11.310 A, 108 atoms)

and a vacuum of 10 A separating images along the surface normal

direction. We adopted PBE lattice parameters from our previous

work.12,15 Due to the large size of the simulation cells, reciprocal

space sampling was restricted to the G-point in all cases.

Car–Parrinello16 molecular dynamics simulations were per-

formed using a timestep of 4 a.u., a fictitious electron mass of

400 a.u. and the real hydrogen mass of 1 AMU. A Nose–

Hoover thermostat with an oscillation frequency of 20 THz

was used to impose a temperature of 400 K.

Acknowledgements

This work was supported by DoE-BES, Chemical Sciences, Geo-

sciences and Biosciences Division under Contract No. DE-FG02-

12ER16286. This research used resources of the National Energy

Research Scientific Computing Center, which is supported by the

Office of Science of theU. S. Department of Energy under Contract

No. DE-AC02-05CH11231. Use of the center for Nanoscale

Materials was supported by the U. S. Department of Energy,

Office of Science, Office of Basic Energy Sciences, under contract

No. DE-AC02-06CH11357. We also acknowledge the use of

the TIGRESS high performance computer center at Princeton

University, which is jointly supported by the Princeton Institute

for Computational Science and Engineering and the Princeton

University Office of Information Technology.

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